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November 2019 Reducibility of Equivalence Relations Arising from Nonstationary Ideals under Large Cardinal Assumptions
David Asperó, Tapani Hyttinen, Vadim Kulikov, Miguel Moreno
Notre Dame J. Formal Logic 60(4): 665-682 (November 2019). DOI: 10.1215/00294527-2019-0024

Abstract

Working under large cardinal assumptions such as supercompactness, we study the Borel reducibility between equivalence relations modulo restrictions of the nonstationary ideal on some fixed cardinal κ. We show the consistency of Eλ-clubλ++,λ++, the relation of equivalence modulo the nonstationary ideal restricted to Sλλ++ in the space (λ++)λ++, being continuously reducible to Eλ+-club2,λ++, the relation of equivalence modulo the nonstationary ideal restricted to Sλ+λ++ in the space 2λ++. Then we show that for κ ineffable Ereg2,κ, the relation of equivalence modulo the nonstationary ideal restricted to regular cardinals in the space 2κ is Σ11-complete. We finish by showing that, for Π21-indescribable κ, the isomorphism relation between dense linear orders of cardinality κ is Σ11-complete.

Citation

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David Asperó. Tapani Hyttinen. Vadim Kulikov. Miguel Moreno. "Reducibility of Equivalence Relations Arising from Nonstationary Ideals under Large Cardinal Assumptions." Notre Dame J. Formal Logic 60 (4) 665 - 682, November 2019. https://doi.org/10.1215/00294527-2019-0024

Information

Received: 5 August 2017; Accepted: 18 July 2018; Published: November 2019
First available in Project Euclid: 14 September 2019

zbMATH: 07167762
MathSciNet: MR4019866
Digital Object Identifier: 10.1215/00294527-2019-0024

Subjects:
Primary: 03E15
Secondary: 03C45

Rights: Copyright © 2019 University of Notre Dame

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Vol.60 • No. 4 • November 2019
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